Analysis of Frequency Response and Scale-Factor of Tuning Fork Micro-Gyroscope Operating at Atmospheric Pressure

This paper presents a theoretical analysis of mechanical and electrical noise in the sense channel of micro-electromechanical systems (MEMS) vibratory gyroscopes. Closed-form expressions for the power spectral density (PSD) of the noise equivalent rate (NER) of gyroscopes in the open-loop and the force-rebalance operations are derived by using an averaged PSD model and an equivalent transfer function. The obtained expressions are verified through numerical simulations, demonstrating close agreements between the analytic and the numerical models. Based on the derived expressions for the PSD of the NER, the impacts of the modal frequency split, quality factor, and the gain of the feedback forcer, as well as the gain of the signal conditioning circuit, on the gyroscope noise characteristics are theoretically analyzed. In addition, the angle random walk (ARW) and the standard deviation of the NER are also discussed through the PSD models. Finally, the effects of the loop closing, the mode matching, and the gain of the feedback forcer on the PSD of the NER were verified via a MEMS vibratory gyroscope with a tunable modal frequency split.

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“…Considering the modulation–demodulation process shown in Figure 2 , the equivalent transfer function can be expressed as [ 17 ]

where the approximation is taken when

and

.…”

Section: Model Of Sense Channel In Mems Vibratory Gyroscopesmentioning

confidence: 99%

Mechanical and Electrical Noise in Sense Channel of MEMS Vibratory Gyroscopes

Ding

Jia

Gao

et al. 2017

Sensors

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“…MEMS CVGs act as an angular sensor based on the Coriolis principle [ 7 ], energy transfer occurs between two orthogonal modes—the drive mode and the sense mode—when working in normal operating conditions [ 8 ]. For operation, the drive mode realizes the resonant frequency tracking by a phase-locked loop (PLL) and the drive amplitude stabilization by an automatic gain control (AGC) loop [ 9 ]; the sense mode obtains the information about the input angular rate. In general, the drive mode is ideally completely orthogonal to the sense mode [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

Online Compensation of Phase Delay Error Based on P-F Characteristic for MEMS Vibratory Gyroscopes

Liu

Qin

2022

Micromachines

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In this paper, an online compensation method of phase delay error based on a Phase-Frequency (P-F) characteristic has been proposed for MEMS Coriolis Vibratory Gyroscopes (CVGs). At first, the influences of phase delay were investigated in the drive and sense mode. The frequency response was acquired in the digital control system by collecting the demodulation value of drive displacement, which verified the existence and influence of the phase delay. In addition, based on the P-F characteristic, that is, when the phase shift of the nonresonant drive force through the resonator is almost 0° or 180°, the phase delay of the gyroscope is measured online by injecting a nonresonant reference signal into the drive-mode dynamics. After that, the phase delay is self-corrected by adjusting the demodulation phase angle without affecting the normal operation of the gyroscopes. The approach was validated with an MEMS dual-mass vibratory gyroscope under double-loop force-to-rebalance (in-phase FTR and quadrature FTR) closed-loop detection mode and implemented with FPGA. The measurement results showed that this scheme can detect and compensate phase delay to effectively eliminate the effect of the quadrature error. This technique reduces the zero rate output (ZRO) from −0.71°/s to −0.21°/s and bias stability (BS) from 23.30°/h to 4.49°/h, respectively. The temperature sensitivity of bias output from −20 °C to 40 °C has reached 0.003 °/s/°C.

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“…To avoid vibration-induced output errors, tuning fork gyroscopes (TFGs) are designed to eliminate linear vibrations output as a common mode signal by differential sensing. TFGs have two identical masses that vibrate out of phase [ 11 ], which cancel common-mode noises and double the amplitude of the output signal compared to conventional MVGs. In general, TFGs are considered to be insensitive to vibrations [ 12 , 13 ].…”

Section: Introductionmentioning

confidence: 99%

Vibration-Induced Errors in MEMS Tuning Fork Gyroscopes with Imbalance

Fang

Dong

Zhao

et al. 2018

Sensors

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This paper discusses the vibration-induced error in non-ideal MEMS tuning fork gyroscopes (TFGs). Ideal TFGs which are thought to be immune to vibrations do not exist, and imbalance between two gyros of TFGs is an inevitable phenomenon. Three types of fabrication imperfections (i.e., stiffness imbalance, mass imbalance, and damping imbalance) are studied, considering different imbalance radios. We focus on the coupling types of two gyros of TFGs in both drive and sense directions, and the vibration sensitivities of four TFG designs with imbalance are simulated and compared. It is found that non-ideal TFGs with two gyros coupled both in drive and sense directions (type CC TFGs) are the most insensitive to vibrations with frequencies close to the TFG operating frequencies. However, sense-axis vibrations with in-phase resonant frequencies of a coupled gyros system result in severe error outputs to TFGs with two gyros coupled in the sense direction, which is mainly attributed to the sense capacitance nonlinearity. With increasing stiffness coupled ratio of the coupled gyros system, the sensitivity to vibrations with operating frequencies is cut down, yet sensitivity to vibrations with in-phase frequencies is amplified.

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Analysis of Frequency Response and Scale-Factor of Tuning Fork Micro-Gyroscope Operating at Atmospheric Pressure

Cited by 6 publications

References 24 publications

Mechanical and Electrical Noise in Sense Channel of MEMS Vibratory Gyroscopes

Mechanical and Electrical Noise in Sense Channel of MEMS Vibratory Gyroscopes

Online Compensation of Phase Delay Error Based on P-F Characteristic for MEMS Vibratory Gyroscopes

Vibration-Induced Errors in MEMS Tuning Fork Gyroscopes with Imbalance

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